Consider the following fx 3X gx x2 5 Find the function fo

Consider the following. f(x) = 3^X, g(x) = x^2 + 5 Find the function fog and its domain. (Enter your answer for domain in interval notation.) Find the function gof and its domain. (Enter your answer for domain in interval notation.)

Solution

f(x) = 3^x ; g(x) = x^2 +5

a) ( f o g)(x) :

(f o g)(x) = 3^(x^2 +5)

Domain :all real x

(- inf , inf)

b) ( g o f )(x)

( g o f)(x) = (3^x)^2 +5 = 3^2x +5

Domain : all real x

(- inf , inf)